I can't believe I haven't found this simple solution anywhere on stack overflow yet, it is by far the most useful. Changing the Document or DocumentFilter does not work for JFormattedTextField. Peter Tseng's answer comes very close.
NumberFormat longFormat = NumberFormat.getIntegerInstance();
NumberFormatter numberFormatter = new NumberFormatter(longFormat);
numberFormatter.setValueClass(Long.class); //optional, ensures you will always get a long value
numberFormatter.setAllowsInvalid(false); //this is the key!!
numberFormatter.setMinimum(0l); //Optional
JFormattedTextField field = new JFormattedTextField(numberFormatter);